No. Taxes from the people are the fuel that powers the federal government. If the federal government isn't working, then why should the people be responsible to provide the fuel? To move forward, the government should take an oath to always work for the people, and this means not quitting in times of disagreement. If the tax dollars were shut off in times of government shut down, you can bet the federal government would be much more likely to come up with bipartisan solutions.
No, people should not have to pay taxes if the governmnet is not working, because the people pay taxes only so that government can do their job. The purpose of government is only to protect people and property locally, and also to provide for a common defense against international agressors. If the government is not doing those things, there is no reason to pay them.